Problem: Solve for $x$ and $y$ using substitution. ${-x-3y = 0}$ ${y = -3x+8}$
Solution: Since $y$ has already been solved for, substitute $-3x+8$ for $y$ in the first equation. ${-x - 3}{(-3x+8)}{= 0}$ Simplify and solve for $x$ $-x+9x - 24 = 0$ $8x-24 = 0$ $8x-24{+24} = 0{+24}$ $8x = 24$ $\dfrac{8x}{{8}} = \dfrac{24}{{8}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {y = -3x+8}\thinspace$ to find $y$ ${y = -3}{(3)}{ + 8}$ $y = -9 + 8$ $y = -1$ You can also plug ${x = 3}$ into $\thinspace {-x-3y = 0}\thinspace$ and get the same answer for $y$ : ${-}{(3)}{ - 3y = 0}$ ${y = -1}$